The following technique has been known as a data hiding method with a statistical approach. First, two pixel point arrays, hereinafter called {an} and {bn}, are selected from the image data. Each respective pixel point array is composed of a number "n" of pixel points. Then, an embedding operation is performed by adding a fixed value c to the value v(an) of n pixels in point array {an}, while subtracting the fixed value c from the value v (bn) of "n" pixels in the other point array {bn}. Thus at each pixel "n", the value of the new array vO(an) and vO(bn) are given by EQU v0 (an)=v (an)+c EQU v0 (bn)=v (bn)-c [Equation 1]
Whether or not embedding is conducted in image data is determined by calculating the average difference between the values of n pixels in both point arrays, and based on its result, as represented in the following formula. ##EQU1##
That is, when an average is calculated for the differences between values of pixels when the number "n" is high enough such that a statistical property appears, it is expected that the average converges to zero if no addition (embedding) is conducted. On the other hand, if the addition (embedding) is conducted, it is expected that the average becomes a fixed value of 2c. Accordingly, whether or not the embedding operation is performed is determined on the basis of a fact whether the average is closer to 0 or 2c, within a set threshold value.
The information to be embedded is one bit, and the positions of the two selected pixel point arrays are confidential. These are known only to the person who performs the embedding (addition) operation. Since the average 2c cannot be retrieved by a person other than the person who performs the embedding operation unless the positions of pixel point arrays can be identified, the fact that this value can be extracted proves that the person is the owner of the data.
However, a problem with this conventional technique that uses the statistical approach, lies in that the identification of who is the owner of data can be easily made unclear by conducting a new embedding operation. That is, even if a third party does not manipulate the pixel value in the pixel point array known only to the owner, the average 2c can be newly produced in two other suitable pixel point arrays by selecting such pixel point arrays, and conducting the embedding operation on their pixel values. Therefore, when the third party who performed such operation falsely claims that he/she himself/herself is the owner based on the average that is calculated from the point array identified by him or her, the conventional technique cannot prove who is the genuine owner.
Another problem lies in that sufficient consideration is not given to the embedding operation and deterioration of image quality caused by it. Even if the same value c is added or subtracted, significant difference may occur in deterioration of visual image quality because of certain characteristics of the image quality. Therefore, it is preferable to adaptively change the amount of embedding, (c), depending on the characteristics of image quality. That is, it is preferable to adaptively select the fixed value c and the number of pixels N in the pixel point arrays.